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Mixed costs contain both a fixed component and a variable component. In order khổng lồ determine the two components, managers must separate the mixed cost into the two manageable components--fixed costs và variable costs. There are a handful of methods used by managers to lớn achieve this. The process of breaking mixed costs into fixed & variable portions allows managers to use the costs lớn predict & plan for the future given the insight on that cost behavior provides. Managers label the process of separating mixed costs into fixed and variable components, cost estimation.

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**Cost Estimation Methods**

The four methods of cost estimation lớn be discussed in managerial accounting are listed below. The first three will be covered in this chapter, with regression covered in the next chapter.

Account analysis

Scatter graphs

High-low method

Linear regression

Cost estimation methods are necessary only for costs that are identified as mixed costs. There is no need to apply an estimation method to lớn break a cost into fixed và variable portions if you have already determined it is solely fixed or solely variable. Even though actual data may be used to determine the fixed & variable components of a mixed costs, all four methods produce*estimates*of amounts of fixed và variable costs.

**The Goal of Cost Estimation**

The ultimate goal of cost estimation is khổng lồ determine the amount of fixed và variable costs so that a cost formula can be used to predict future costs. The cost formula, or cost equation, is the output đầu ra of the cost estimation process. Because you have only one variable (number of units), the formula will be a straight line, or linear equation. (You should remember the concept of functions from your high school algebra classes.1) The formula that represents the equation of a line will appear in the format of:

y = mX + b

where y = total cost

m = the slope of the line, i.e., the unit variable cost

X = the number of units of activity

b = the y-intercept, i.e., the total fixed costs

Recall that the y = VCx + TFC is the equivalent equation used in accounting for estimating costs.

The total cost side of the equation (y) can also be expressed as f(x) so that the formula appears as:

f(x) = VCx + TFC

As such, the equation is often referred to lớn as a function. In accounting, it is referred to lớn as a cost function because the 'y' equates to lớn total cost.

Determining a linear function is useful in predicting cost amounts at different levels of activity. This is useful because managers must be able khổng lồ predict costs lớn plan for future operations. This is often accompanied by what-if analysis that assists with the preparation of budgets, pricing of products or services, và other key management functions.

**Cost Equation Components**

Your goal it lớn determine the cost equation for a particular cost. Because our ultimate goal is khổng lồ determine the 'total' cost, the cost equation must use cost amounts that remain the same at every màn chơi of activity, as you do want to be able to lớn calculate the total cost at every activity level. As such, the cost equation will contain the variable cost*per unit*and*total*fixed costs. These two amounts remain the same at all levels of activity within the relevant range.

The VC component of the cost equation is displayed with two decimals in standard khung because this variable cost amount is a unit cost (and unit costs are always displayed with two decimal places). The TFC component of the cost equation is displayed with no decimals.

The trương mục analysis method of estimating fixed and variable costs is likely the approach you have used to lớn identify cost behavior so far in your study of managerial accounting, by simply looking at a cost and guessing its most likely type of cost behavior. This method requires considerable subjective judgment and insight. It is most often used by accountants or managers who are familiar with the nature of costs within a general ledger tài khoản (often multiple accounts). Tài khoản analysis is the only method you can use khổng lồ estimate costs when only one one period of data are known.

The trương mục analysis approach requires that each individual cost is examined & based on judgment, is categorized as a fixed or a variable cost. V*ariable cost per unit*is calculated by dividing the total of all variable costs by the number of units produced/sold.

Total Variable Costs | = Variable cost per unit |

Numberof Units Produced/Sold |

The variable cost per unit is plugged into the cost formula, y = VCx + TFC, as the variable cost (VC). The fixed costs are totaled separately và replace the y-intercept (TFC) component of the equation. This results in a cost equation that can be used khổng lồ estimate costs for future periods.

*Note that the determination of 'cost per unit' is literal. The calculation is performed exactly how it reads: 'Cost' is on the numerator; 'Per' means divide; and 'units' appears on the denominator.*

Home Shine is estimating its fixed & variable costs. The following costs were incurred during the month of May by home Shine when 200 homes were cleaned:

Cleaning supplies | $2,400 |

Hourly wages | 4,850 |

Depreciation - cleaning equipment | 650 |

Manager’s salary | 1,400 |

Auto commuting expenses | 1,600 |

Office rent | 850 |

Total costs | $11,750 |

Use the tài khoản analysis method to lớn determine the total cost equation for home Shine.

**Solution**

**Step 1:**Classify each amount as variable or fixed based on judgment. By definition, variable costs increase in total when more activity occurs. The activity for this problem is number of homes cleaned. By definition, fixed costs are the same in total regardless of the activity level.

*Cleaning supplies*= variable cost. The total cost of cleaning supplies increases when more homes are cleaned.

*Hourly wages*= variable cost. The total cost of hourly wages increases when more homes are cleaned.

*Depreciation*= The total cost of depreciation is $650 regardless of the number of homes cleaned.

*Manager's salary*= The manager's salary is the same regardless of the number of hours worked or the number of homes cleaned.

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*Auto commuting expenses*= variable cost. The total cost of commuting expenses such as gasoline and maintenance increases when more homes are cleaned.

*Office rent*= The monthly office rent is the same regardless of the number of homes cleaned.

**Step 2:**Total the amount of the costs you identified as variable.

$2,400 + $4,850 + $1,600 = $8,850

Calculate*variable cost per unit*by dividing the total of all the variable costs by the number of units (homes) produced/sold (cleaned).

$8,850 | = $44.25 |

200 |

**Step 3:**Total the amount of the costs you identified as fixed costs.

$650 +$1,400 + $850 = $2,900

**Step 4:**Plug your answers lớn steps 2 & 3 into the cost formula by replacing the slope (m) with variable cost per unit & the y-intercept (b) with total fixed costs in the cost equation:

y = 44.25X + 2,900

The cost equation indicates that the total cost of cleaning homes is $44.25 per home plus a monthly cost of $2,900.

**Scatter Graph Method**

Creating a scatter graph is another method of estimating fixed and variable costs. It provides a good visual picture of the total costs at different activity levels. However, it is often hard to visualize the line through the data points, especially if the data is varied. This approach requires multiple data points and requires five steps:

**Step 1:**Draw a graph with the total cost on the y-axis and the activity (units) on the x-axis.Plot the total cost points for each activity points.

**Step 2:**Visualize và draw a straight line through the points.

**Step 3:**Determine variable costs per unit by identifying the slope thorough a measure of rise over run.

Rise | = Variable cost per unit |

Run |

**Step 4:**Identify where the line crosses the y-axis. This is the total fixed cost amount.

**Step 5:**Plug your answers to steps 3 & 4 into the cost formula by replacing the slope (m) with variable cost per unit & the y-intercept (b) with total fixed costs in the following format:

y = VCx + TFC

**High-Low Method**

The high-low method uses the highest and lowest activity levels over a period of time to lớn estimate the portion of a mixed cost that is variable and the portion that is fixed. Because this method uses only the high & low activity levels to lớn calculate the variable & fixed costs, it may be misleading if the high và low activity levels are not representative of the normal activity, i. E., they may be extremes, or outliers. For example, if most data points lie in the range of 60 khổng lồ 90 percent for a particular accounting test, & one student scored a 20, the use of the low point might distort the actual expectation of costs in the future. The high-low method is most accurate when the costs incurred at the high & low levels of activity are representation of the majority of the other points. The steps below guide you through the high-low method:

**Step 1:**Determine which set of data represents the total cost (dependent variable, y) and which represents the activity (independent variable, x). Find the lowest & highest activity points in the data representing the x variable.

**Step 2:**Determine variable costs per unit by using the mathematical slope formula, by dividing the change in cost by the change in activity:

Y2 -Y1 | = Variable cost per unit |

X2 - X1 |

Where X2 is the high activity level

X1 is the low activity level

Y2 is the total cost at the high activity level

Y1 is the total cost at the low activity level

**Step 3:**Plug your answer to lớn step 2 and the amounts from*either*the high or the low point into the cost formula by replacing the slope (VC) with the variable cost per unit, the total cost (at the highest activity point) for the y variable, and the high activity for the x variable. Then solve for fixed costs (TFC).

**Step 4:**Plug your answers lớn steps 2 & 3 into the cost formula by replacing the slope (VC) with variable cost per unit và the y-intercept (TFC) with total fixed costs in the following format:

y = VC x + FC

If you have forgotten algebra concepts relating lớn the slope-intercept form, you can review those conceptshere.2

**High-Low Method Walk Through Problem**

Information concerningunits sold và total delivery costs for Bridges, Inc. For five months of năm ngoái appears below:

Units | Costs | |

January | 1,200 | $74,150 |

February | 1,150 | 71,000 |

March | 1,190 | 72,400 |

April | 1,300 | 80,600 |

May | 1,310 | 79,040 |

Use the high-low method to lớn answer the following:

A. How much is the variable cost per unit?

B.How much are total fixed costs?

C. Write the cost equation in proper form.

**Solution**

q**Step 1:**The*Units*column is the activity. The*Costs*column is the Total cost. Because the*Units*column represents activity, select the high & low data points from the*Units*column. May generated the largest activity with 1,310 units, & February generated the lowest activity with 1,150 units.

**Step 2:**Use the slope formula by subtracting the smallest from the largest activity on the denominator. Use the corresponding total costs for May and February và subtract the smallest from the largest cost on the numerator:

Y2 - Y1 | = | $79,040 - $71,000 | = | $50.25 per unit |

Y2 - Y1 | 1,310 - 1,150 |

The variable cost per unit is $50.25.

**Step 3:**Select either of the two data points that you chose in Step 1 to plug into the cost equation. Both data points will result in the same answer. Using the low data point (February), the total cost of $71,000 is substituted for “y” in the cost equation, & 1,150 units is substituted for 'x', the units variable. Substitute the unit variable cost from step 2 into the formula for “VC.” Substitute the number of activity units for the low data point for “x”You should now have the following equation:

y = VC x + TFC

71,000 = (50.25 x 1,150) + TFC

Solve fortotal fixed costs (TFC), which results in $13,212.50.

**Step 4:**Write the cost formula in standard form by plugging in the variable cost per unit và total fixed cost as follows:

y = 50.25x+ 13,213

The standard format is to express variable cost per unit using two decimal places & total fixed costs with no decimal places.

**Using a Cost Equation to lớn Estimate Future Costs**

Once a cost equation is determined, it can be used lớn estimate costs at various levels of activity. For example, assume Bridges, Inc. Expects khổng lồ sell 1,240 units of product in June. Using the total cost equation determined in the high-low method walk through problem, the total estimated cost would be: